Affiliation:
1. School of Mathematics and Statistics Beijing Institute of Technology Beijing China
2. Freie Universität Berlin and Berlin Mathematical School Germany
3. School of Mathematics Shandong University Jinan China
4. Data Science Institute Shandong University Jinan China
Abstract
AbstractFor a ‐vertex graph and an ‐vertex graph , an ‐tiling in is a collection of vertex‐disjoint copies of in . For , the ‐independence number of , denoted , is the largest size of a ‐free set of vertices in . In this article, we discuss Ramsey–Turán‐type theorems for tilings where one is interested in minimum degree and independence number conditions (and the interaction between the two) that guarantee the existence of optimal ‐tilings. Our results unify and generalise previous results of Balogh–Molla–Sharifzadeh [Random Struct. Algoritm.
49 (2016), no. 4, 669–693], Nenadov–Pehova [SIAM J. Discret. Math. 34 (2020), no. 2, 1001–1010] and Balogh–McDowell–Molla–Mycroft [Comb. Probab. Comput. 27 (2018), no. 4, 449–474] on the subject.
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Natural Science Foundation of Shandong Province
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software
Cited by
2 articles.
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